13.1 Lines, Rays, and Angles

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Name Geometry and Measurement—4.6.A 13.1 MATHEMATICAL PROCESSES Lines, Rays, and Angles 4.1.D, 4.1.E ? Essential Question How can you identify and draw points, lines, line segments, rays, and angles?

UnlockUnlock thethe ProblemProblem

Everyday things can model geometric figures. For example, the period at the end of this sentence models a point. A solid painted stripe in the middle of a straight road models a line.

Term and Definition Draw It Read It Write It Example A A A point is an exact location in A point point space.

‹__› A line is a straight path of points line BC BC __ that continues without end in B C ‹ › line CB CB both directions.

___ A line segment is part of a line line segment DE DE between two endpoints. D E ___ line segment ED ED

__ FG FG› A ray is a part of a line that has F G ray one endpoint and continues without end in one direction.

___ Activity 1 Draw and label JK . Math Talk Mathematical Processes Explain how lines, line segments, and rays ____ are related.

___ • Is there another way to name JK ? Explain.

Module 13 449 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (c) ©Photo 24/Getty Images: (b) ©pm/Alamy (c) ©Photo 24/Getty Images: © Houghton Mifflin Harcourt Publishing Company • Image Credits: Angles

Term and Definition Draw It Read It Write It Example An angle is formed by two rays or P angle PQR ∠PQR line segments that have the same angle RQP ∠RQP endpoint. The shared endpoint is called the vertex. angle Q ∠Q

Q R

You can name an angle by the vertex. When you name an angle using 3 points, the vertex is always the point in the middle.

Angles are classified by the size of the opening between the rays. A right angle forms A straight angle forms An acute angle is less An obtuse angle is a square corner. a line. than a right angle. greater than a right angle and less than a straight angle.

Activity 2 Classify an angle.

Materials ■ paper To classify an angle, you can compare it to a right angle. Make a right angle by using a sheet of paper. Fold the paper twice evenly to model a right angle. Use the right angle to classify the angles below. Write acute, obtuse, right, or straight. a. b. c. d.

450 © Houghton Mifflin Harcourt Publishing Company Name

ShareShare andand ShowShow ___ 1. Draw and label AB in the space at the right. ___ AB is a ____ .

Draw and label an example of the figure. ‹___› 2. XY 3. obtuse ∠K 4. right ∠CDE

Use Figure M for 5 and 6. 5. Name a line segment. 6. Name a right angle. TU

V W Figure M

ProblemProblem SolvingSolving

Use the picture of the bridge for 7 and 8.

7. Classify ∠A. 8. Which angle appears to be obtuse?

9. Use Diagrams How many different E F angles are in Figure X? List them. D

ACB Figure X

10. Multi-Step What’s the Error? Vanessa drew the angle at the right and named it ∠TRS. Explain why Vanessa’s name R for the angle is incorrect. Write a correct name for the angle. S

Module 13 • Lesson 1 451 © Houghton Mifflin Harcourt Publishing Company • Image Credits: MathematicalM Processes MModel ¥ Reason ¥ Communicate DailyDaily AssessmentAssessment TaskTask

Fill in the bubble completely to show your answer.

11. What type of angle is ∠ABC?

A acute C B right

C obtuse A B D straight

12. Which names a straight angle in the figure below? W X

T Y S

A ∠XTW C ∠STY B ∠STX D ∠WTS

13. Multi-Step What is the total number of acute angles in the figures shown below? T D Z A X Y

S BC

A 2 C 4 B 8 D 6

TEXAS Test Prep 14. Which of the following terms best describes the figure below?

A ray C line B line segment D angle

452 © Houghton Mifflin Harcourt Publishing Company Geometry and Measurement—4.6.A Homework MATHEMATICAL PROCESSES 4.1.D, 4.1.E and Practice Name

13.1 Lines, Rays, and Angles

Draw and label an example of the figure. ___› 1. AB 2. acute ∠J 3. right ∠ABC

‹__› ___ 4. JK 5. obtuse ∠XYZ 6. PQ

Use figure A for 7 and 8.

7. Name an acute angle. 8. Name an obtuse angle. A B

D ProblemProblem SolvingSolving Figure A Use the bridge drawing for 9 and 10.

9. Classify ∠B

10. Jenny thinks that ∠C is a right angle. Explain why Jenny’s name for the angle is incorrect. Write a correct name for the angle.

Fill in the bubble completely to show your answer. 11. What type of angle is ∠XYZ? 12. Which names an obtuse angle in the figure below? X T

Z Y Z X Y S A right

B acute A ∠TZS C straight B ∠SZY D obtuse C ∠XZT D ∠TZY

13. Which names an acute angle TU 14. Which of the following terms best in the figure to the right? describes the figure below? ∠ V A VWU AB W B ∠VTU Figure M A angle C ∠TUW B line segment D ∠WUT C ray D line

15. Multi-Step What is W 16. Multi-Step How X E the total number many right angles F D of rays in the T are in Figure X? figures to the right? Y S A 4 ACB X A 6 Figure B 2 B 2 D A C 3 C 5 D 1 D 7 BC